Geodesic distance gets particularly interesting to me (and others) when you try to use it to instantiate concentric distance loops on the surface. I watched this guys video ... and he didn't go there. I think it's the hard part ... because of aliasing and such. Do you understand what I'm getting at ?

Cycling colors would just mean repeating the rainbow more times over a given surface distance. More banding.

In my mind ... this probably means increasing the resolution of the underlaying mesh so that we have more discrete places to put rainbow bands. If were are both nativeEenglish speakers ... we need to stick to words and metaphors like RAINBOW and repeat. But is you really like code ... I can just send you the code snippet ... since it is very short.

It seems that this thing can be used for creating new topology on objects too. Imagine that instead of the displacement circles around the body, you create simple edge loops. If such a thing can be achieved then remains finding a way of creating the vertical lines-edges.